Subgroups — C₇×C₃₁×C₃⋊Dic₃ #21462960

Order 7812.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃×C₃₁	—	3	4	no	maximal
3	C₃²×C₇×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₃₁	D₃	1	4	yes	—
5	C₃₁×C₃⋊Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₄×C₇×C₃₁	—	9	1	no	Hall
7	C₃×C₇×C₃₁	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₃₁	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₃₁	C₃⋊D₃	1	1	yes	characteristic
10	Dic₃×C₃₁	—	3	4	no	—
11	C₃²×C₃₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₃⋊Dic₃	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇×C₃₁	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₃₁	D₃×C₇	1	4	yes	—
15	C₂×C₃²×C₇	C₂×C₃₁	1	1	yes	characteristic
16	C₄×C₃₁	—	9	1	no	Hall
17	C₃×C₃₁	C₇×Dic₃	1	4	yes	complemented
18	C₇×Dic₃	—	3	4	no	—
19	C₃²×C₇	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	C₇×C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃×C₇	D₃×C₃₁	1	4	yes	—
22	C₃⋊Dic₃	C₇×C₃₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃₁	C₇×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₄×C₇	—	9	1	no	Hall
25	C₃×C₇	Dic₃×C₃₁	1	4	yes	complemented
26	C₂×C₃²	C₂×C₇×C₃₁	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₃×C₃₁	1	1	yes	characteristic
28	Dic₃	—	3	4	no	—
29	C₃²	C₄×C₇×C₃₁	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃₁×C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	D₃×C₇×C₃₁	1	4	yes	—
32	C₄	—	9	1	no	Sylow
33	C₃	C₇×Dic₃×C₃₁	1	4	yes	complemented
34	C₂	C₇×C₃⋊D₃×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇×C₃₁	C₃⋊D₃
commutator, hypocenter	C₃²	C₄×C₇×C₃₁
Frattini	C₂	C₇×C₃⋊D₃×C₃₁
Fitting, socle	C₂×C₃²×C₇×C₃₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₇×C₃₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃²×C₇×C₃₁	C₄	semidirect
5. C₃₁×C₃⋊Dic₃	C₇	direct (N × H)
7. C₃×C₇×C₃₁	Dic₃	semidirect
11. C₃²×C₃₁	C₄×C₇	semidirect
12. C₇×C₃⋊Dic₃	C₃₁	direct (N × H)
13. C₇×C₃₁	C₃⋊Dic₃	direct (N × H)
17. C₃×C₃₁	C₇×Dic₃	semidirect
19. C₃²×C₇	C₄×C₃₁	semidirect
22. C₃⋊Dic₃	C₇×C₃₁	direct (N × H)
23. C₃₁	C₇×C₃⋊Dic₃	direct (N × H)
25. C₃×C₇	Dic₃×C₃₁	semidirect
29. C₃²	C₄×C₇×C₃₁	semidirect
30. C₇	C₃₁×C₃⋊Dic₃	direct (N × H)
33. C₃	C₇×Dic₃×C₃₁	semidirect

Subgroups — C7×C31×C3⋊Dic3 #21462960

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₃₁×C₃⋊Dic₃ #21462960